This problem is in my textbook, and seem very easy, but I cannot imagine how can we find the distance from the point to the $span U$. Because $span U$ is not like a plane, a line... in geometry (in my thinking).

1 Answer
1

The elements of U are in the form $(a,b,-b,-a)$. The distance from $(a,b,-b,-a)$ to $(2,0,2,0)$ is $(a-2)^2+b^2+(-b-2)^2+a^2$ Now minimize the last expression by minimizing $(a-2)^2+a^2$ and minimizing $(-b-2)^2+b^2$